<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
<html>
<!-- This manual is for FFTW
(version 3.3.10, 10 December 2020).

Copyright (C) 2003 Matteo Frigo.

Copyright (C) 2003 Massachusetts Institute of Technology.

Permission is granted to make and distribute verbatim copies of this
manual provided the copyright notice and this permission notice are
preserved on all copies.

Permission is granted to copy and distribute modified versions of this
manual under the conditions for verbatim copying, provided that the
entire resulting derived work is distributed under the terms of a
permission notice identical to this one.

Permission is granted to copy and distribute translations of this manual
into another language, under the above conditions for modified versions,
except that this permission notice may be stated in a translation
approved by the Free Software Foundation. -->
<!-- Created by GNU Texinfo 6.7, http://www.gnu.org/software/texinfo/ -->
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
<title>What FFTW Really Computes (FFTW 3.3.10)</title>

<meta name="description" content="What FFTW Really Computes (FFTW 3.3.10)">
<meta name="keywords" content="What FFTW Really Computes (FFTW 3.3.10)">
<meta name="resource-type" content="document">
<meta name="distribution" content="global">
<meta name="Generator" content="makeinfo">
<link href="index.html" rel="start" title="Top">
<link href="Concept-Index.html" rel="index" title="Concept Index">
<link href="index.html#SEC_Contents" rel="contents" title="Table of Contents">
<link href="FFTW-Reference.html" rel="up" title="FFTW Reference">
<link href="The-1d-Discrete-Fourier-Transform-_0028DFT_0029.html" rel="next" title="The 1d Discrete Fourier Transform (DFT)">
<link href="Wisdom-Utilities.html" rel="prev" title="Wisdom Utilities">
<style type="text/css">
<!--
a.summary-letter {text-decoration: none}
blockquote.indentedblock {margin-right: 0em}
div.display {margin-left: 3.2em}
div.example {margin-left: 3.2em}
div.lisp {margin-left: 3.2em}
kbd {font-style: oblique}
pre.display {font-family: inherit}
pre.format {font-family: inherit}
pre.menu-comment {font-family: serif}
pre.menu-preformatted {font-family: serif}
span.nolinebreak {white-space: nowrap}
span.roman {font-family: initial; font-weight: normal}
span.sansserif {font-family: sans-serif; font-weight: normal}
ul.no-bullet {list-style: none}
-->
</style>


</head>

<body lang="en">
<span id="What-FFTW-Really-Computes"></span><div class="header">
<p>
Previous: <a href="Wisdom.html" accesskey="p" rel="prev">Wisdom</a>, Up: <a href="FFTW-Reference.html" accesskey="u" rel="up">FFTW Reference</a> &nbsp; [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Concept-Index.html" title="Index" rel="index">Index</a>]</p>
</div>
<hr>
<span id="What-FFTW-Really-Computes-1"></span><h3 class="section">4.8 What FFTW Really Computes</h3>

<p>In this section, we provide precise mathematical definitions for the
transforms that FFTW computes.  These transform definitions are fairly
standard, but some authors follow slightly different conventions for the
normalization of the transform (the constant factor in front) and the
sign of the complex exponent.  We begin by presenting the
one-dimensional (1d) transform definitions, and then give the
straightforward extension to multi-dimensional transforms.
</p>
<table class="menu" border="0" cellspacing="0">
<tr><td align="left" valign="top">&bull; <a href="The-1d-Discrete-Fourier-Transform-_0028DFT_0029.html" accesskey="1">The 1d Discrete Fourier Transform (DFT)</a></td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="The-1d-Real_002ddata-DFT.html" accesskey="2">The 1d Real-data DFT</a></td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="1d-Real_002deven-DFTs-_0028DCTs_0029.html" accesskey="3">1d Real-even DFTs (DCTs)</a></td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="1d-Real_002dodd-DFTs-_0028DSTs_0029.html" accesskey="4">1d Real-odd DFTs (DSTs)</a></td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="1d-Discrete-Hartley-Transforms-_0028DHTs_0029.html" accesskey="5">1d Discrete Hartley Transforms (DHTs)</a></td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="Multi_002ddimensional-Transforms.html" accesskey="6">Multi-dimensional Transforms</a></td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
</table>




</body>
</html>
